More than 2/3 of animals are transported on just four airlines: Alaska, Delta, American, and United. United was responsible for transporting a plurality (27%) of all animals in 2017, so we would expect -- from sheer volume alone -- for more pets to die on United flights. So, the question is, "Do a statistically disproportionate number of animals die on United?" In 2017, sadly, the answer is yes.
An investigation by Business Insider found that, "United had more pet deaths in 2016 than any other major US airline." Given United's recent public relations debacle, is this true, too? Technically yes, but statistically no. Becasue it's the statistics that matter, not the raw numbers.